Those are so minor. Most of your points don't make her a leader, and some of them make her look like a bad one.

1. She's a teacher. Just like all of the other X-men. The only difference in this movie is that only she and Wolverine are able to teach. And Wolverine dominates the danger room session.

2. She fails because Wolverine undermines her "leadership."

3. Wolverine is ultimately justified at the end of the movie, like you point out. Storm didn't teach or lead Wolverine.

4. And Beast has to shut her up due to her insensitivity. Does she even mention the cure again in the movie?

5. Of course Storm leads them through the mist... she controls the weather! Using her powers doesn't equate leadership.

6. Very, very minor.

7. Her Eulogy was out place considering how little Xavier and Storm interacted outside of X3. But when all the better developed characters are gone, just give the leftovers to storm.

8. Best moment of leadership, however it's completely shallow. The movie never explores how it affects her to keep it open. Why was there such doom and gloom over the school closing if Storm can just say one sentence and the school stays open?

9. Completely uncarring, unsympathetic, and unlikable... but yeah I guess it was leader-ish.

10. Grasping at straws. They don't show her preparing or motivating the students. Again, it's all Wolverine. He has the leader speech... she does absolutely squat and takes the backseat to Wolverine. And she comes across as cold again.

11. Minor. She pilots the jet in X2 also. And they were all using their powers. It's Wolverine with the strategy, telling everyone to hold the line.

12. Storm learns from Wolverine, but did Wolverine learn from Storm at all?

13. The movie ends with her as headmistress, but it's not developed at all.

As far as her personality goes, I'm not buying the "different aspects of her personality" bit. There isn't anything consistent between the three aspects. She's scared and insecure, then she's angry, and I don't even know what she was in X3. Whereas someone like Cyclops, who had less screen time than her in the movies, is consistent and when he acts the way he does in X3 he's justified.

The sad thing is that I like Storm, and I like Halle Berry. I just think the writing has been weak regarding her in the trilogy. They did amazingly with other characters, but if she's in DOFP I want to see better writing. Unless it's just a cameo.